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Annals of Mathematics, ISSN 0003-486X, 5/2014, Volume 179, Issue 3, pp. 1121 - 1174
It is proved that $\lim_{n\rightarrow \infty }inf(p_{n+1}-p_n)\textless 7\times 10^7$, where pn is the n-th prime. Our method is a refinement of the recent... 
Integers | Cauchy Schwarz inequality | Prime numbers | Arithmetic progressions | Mathematical theorems | Partial sums | Mathematical functions | Factorization | Estimation methods | MATHEMATICS | ARITHMETIC PROGRESSIONS | LARGE MODULI | NUMBERS
Journal Article
Annals of Mathematics, ISSN 0003-486X, 1/2015, Volume 181, Issue 1, pp. 383 - 413
We introduce a refinement of the GPY sieve method for studying prime k-tuples and small gaps between primes. This refinement avoids previous limitations of the... 
Integers | Prime numbers | Admissible sets | Approximation | Eigenvalues | Linear transformations | Eigenfunctions | Polynomials | Coefficients | MATHEMATICS
Journal Article
2017, First edition., ISBN 0198788282, vi, 164 pages
Book
Annals of Mathematics, ISSN 0003-486X, 5/2016, Volume 183, Issue 3, pp. 915 - 933
We show that there exist pairs of consecutive primes less than x whose difference is larger than t(1 + o(1))(log x)(log log x)(log log log log x)(log log log... 
Prime numbers | Mathematical constants | Mathematical functions | Mathematical theorems | Approximation | MATHEMATICS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 10/2018, Volume 745, pp. 36 - 52
We introduce the family of k-gap-planar graphs for k≥0, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges... 
k-quasiplanar graphs | Complete graphs | Beyond planarity k-gap-planar graphs | k-planar graphs | Density results | Recognition problem | LINEAR-TIME | NUMBER | CROSSINGS | EDGES | COMPUTER SCIENCE, THEORY & METHODS | 1-PLANARITY
Journal Article
IEEE Transactions on Industrial Electronics, ISSN 0278-0046, 03/2012, Volume 59, Issue 3, pp. 1367 - 1375
Journal Article
Renewable and Sustainable Energy Reviews, ISSN 1364-0321, 03/2015, Volume 43, pp. 1159 - 1166
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2015, Volume 429, Issue 1, pp. 204 - 232
Let L(s,f) be an L-function associated to a primitive (holomorphic or Maass) cusp form f on GL(2) over Q. Combining mean-value estimates of Montgomery and... 
Selberg Class | L-functions | Gaps between zeros | MATHEMATICS | MATHEMATICS, APPLIED | ZETA-FUNCTIONS | SELBERGS ORTHOGONALITY | MEAN-VALUE | DIRICHLET SERIES | CONSECUTIVE ZEROS | PAIR CORRELATION | Mathematics - Number Theory
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 10/2017, Volume 287, Issue 1, pp. 547 - 554
The bounded gaps property of the prime numbers, as proven by Yitang Zhang, is considered for sequences of lengths of closed geodesics, which by the theory of... 
Mathematics, general | Mathematics | MATHEMATICS | PRIMES
Journal Article
Annals of Mathematics, ISSN 0003-486X, 5/2016, Volume 183, Issue 3, pp. 935 - 974
Let G(X) denote the size of the largest gap between consecutive primes below X. Answering a question of Erdős, we show that $G(X)\geqslant f(X)\frac{logX log... 
Integers | Prime numbers | Arithmetic progressions | Sieving | Mathematical theorems | Cardinality | Infinity | Mathematical congruence | Linear equations | INVERSE THEOREM | MATHEMATICS | ARITHMETIC PROGRESSIONS | GOWERS
Journal Article
Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 03/2008, Volume 77, Issue 11
The calculation of the band gap by density-functional theory (DFT) is examined by considering the behavior of the energy as a function of number of electrons.... 
DISCONTINUITY | PHYSICS, CONDENSED MATTER | NUMBER | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | Physics - Materials Science
Journal Article
Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 02/2015, Volume 91, Issue 6
We address the quantum-critical behavior of two-dimensional itinerant ferromagnetic systems described by spin-fermion models in which fermions interact with... 
ORDER | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | MATERIALS SCIENCE, MULTIDISCIPLINARY | STATE | TRANSITIONS | SPIN-FERMION MODEL | RENORMALIZATION
Journal Article